Pensioners could defer their council tax payments until they die under a plan being considered for England.
The review of council tax continues
It is one of the options Sir Michael Lyons is looking at in his government-commissioned review of local taxation in England.
The idea is that those who own a home could defer payment until after they die and their home is sold.
The Conservatives called it a "sinister death tax". Lib Dems oppose "saddling grieving families with death taxes".
A similar scheme has already been proposed for Northern Ireland, although it would be up to a future devolved assembly to implement it.
Labour MP Clive Betts, who sits on the Commons committee which supervises local government ministers, told BBC Radio 4's World at One, that he backed the idea for England.
"It won't be compulsory. People will be able to pay the tax as they go along. So it is an option that is available for people. I think creating another option is entirely right.
"I think it is very unlikely that even if people chose to defer all or some of their council tax that it is going to take up all the value of their property when they sell it.
"There is still going to be quite a lot left in most cases I am sure."
Conservative local government spokeswoman Caroline Spelman said the problem was that local authority charges had risen by up to 70% since Tony Blair came to power.
"I fear that the elderly, struggling with soaring council tax bills, will be pressured into signing away their homes to the taxman," said Mrs Spelman.
"Vulnerable people face either forfeiting their children's inheritance or have the bailiff knocking on their door for non-payment of rising council taxes.
"If the Government really wanted to help the elderly, it should look to cut their bills by introducing an automatic council tax discount for pensioner households."
An Office of Deputy Prime Minister spokesman said there was no reason to think such a scheme was going to be introduced.
But a spokesman for the Lyons inquiry, due to report in December, said: "Methods of deferral are within the remit of the inquiry and are just one in a range of ideas being considered."
Ability to pay
The Conservatives say that deferring the average Band D bill of £1,214 for 20 years in a row could leave an accumulated bill of £75,986, at current levels of interest.
Liberal Democrat local government spokeswoman Sarah Teather said: "Pensioners get a raw deal... but saddling grieving families with massive death taxes is not the answer. "Tinkering with council tax is not enough. It must be scrapped and replaced with a fair system based on ability to pay."
Professor John Muelbauer, an Oxford University economist who has given evidence to the Lyons inquiry, said the idea was to relieve pressure on pensioners who may be living on very low incomes.
The payments would not necessarily be deferred until death, but may be once a person moved into a cheaper home or residential care, he told the World at One.
He said a similar system operated in Denmark.